Delivery systems for dispensing a beneficial agent to a biological environment of use are known to the prior art. For example, delivery systems comprising a wall that surrounds an internal lumen that houses a thermoresponsive formulation, an expandable driving member and a density member are known in U.S. Pat. Nos. 4,595,583; 4,612,186; 4,624,945; 4,684,524; 4,692,336; 4,717,566; 4,717,568; 4,717,718; 4,772,474; and 4,844,984 all issued to Eckenhoff, Cortese and Landrau, in U.S. Pat. Nos. 4,663,148; 4,663,149; 4,678,467; 4,716,013; 4,781,714; 4,800,056; and 4,814,180 issued to Eckenhoff, Theeuwes, and Deters, and in U.S. Pat. Nos. 4,675,174 and 4,704,118 issued to Eckenhoff. These dispensing systems of the prior art are extraordinarily effective for delivering beneficial agents that are hydrophilic, hydrophobic, lipophilic or lipophobic to a biological environment of use. The delivery systems operate successfully for their intended use, and they can deliver numerous difficult to deliver beneficial agents at a controlled and predictable rate. Sometimes, however, the delivery systems, when in operation in a biological environment of use having a high pressure or high partial pressures of biological or other gases, exhibit a delivery rate that is unpredictable. This is due to a low internal pressure of a gas phase in the delivery system relative to an exterior higher pressure or partial pressure.